Visas for overseas millionaires will be auctioned to the highest bidders or “sold” in exchange for donations to hospitals and universities, under proposals by the Government’s official migration advisers.

Wealthy foreigners would make offers for a proportion of so-called investor visas, which allow them and their families to live in Britain indefinitely.

A second option to be outlined in the report is to offer the visas to millionaires who are willing to endow good causes, such as universities, colleges and hospitals.

The ideas are to be put forward amid concern that the existing investor visa route is not working to